Rarity of the infinite chains in the tree of numerical semigroups
Maria Bras-Amorós, Mariana Rosas-Ribeiro · Semigroup Forum · 2026
Abstract We prove that, for each fixed genus, the proportion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinity. This means that most numerical semigroups have a finite number of descendants in the semigroup tree. This problem has been open since 2009.